Manuel Rios wishes to determine how long it will take an initial deposit of $$$$11$ comma $00011,000$ to double.

a$.$If Manuel earns $1212\%$ annual interest on the$$ deposit, how long will it take for him to double his$$ money?

b$.$How long will it take if he earns only $99\%$ annual$$ interest?$$

c$.$How long will it take if he can earn $1414\%$ annual$$ interest?

d$.$ Reviewing your findings in parts a$,$ b$,$ and c$,$ indicate what relationship exists between the interest rate and the amount of time it will take Manuel to double his money.